energy-efﬁciency of cooperative sensing …...energy-efﬁciency of cooperative sensing schemes 57...

Energy-Efficiency of Cooperative SensingSchemes in Ad Hoc WLAN Cognitive Radios

Reshma Syeda and Vinod Namboodiri

Department of Electrical Engineering & Computer Science,Wichita State University, 1845 Fairmount St., Wichita, KS 67260, USA;e-mail: {rssyeda, vinod.namboodiri}@wichita.edu

Received 13 September; Accepted: 28 September

Abstract

In cognitive radio networks, the secondary users need to coordinate amongthemselves to reap the benefits of cooperative spectrum sensing. In this pa-per, we study and analyze the energy efficiency of two generic cooperativesensing schemes in an ad hoc WLAN backdrop – distributed cooperativesensing scheme and centralized cluster based cooperative sensing scheme.We further propose corresponding enhanced and adaptive versions of thesetwo schemes where only an α fraction of nodes sense in each sensing cycle,as opposed to all the nodes in the network. Using an analytical energy modelfor sensing, we quantify the energy costs of each of these schemes and per-form a comparative numerical analysis to demonstrate the amount of energysavings of the proposed cooperative schemes over their generic counterpartsand non-cooperative schemes.

Keywords: cognitive radio, cooperative sensing, energy efficiency, WLAN.

1 Introduction

The world has witnessed a great deal of change this decade when it comesto wireless technologies. Be it Wi-Fi, WiMAX, WSNs or any other subtechnology belonging to one of these areas, these technologies have per-

Journal of Green Engineering, Vol. 2, 55–83.c© 2011 River Publishers. All rights reserved.

56 R. Syeda and V. Namboodiri

meated so deep into our lives that it is hard to imagine our lifestyles withoutthem. However, with demand comes scarcity. The spectrum allocated to thesetechnologies is greatly limited and hence the scarcity which emphasizes thegreat need to deal with and overcome this issue. Figures 1 and 2 show thespectrum measurements taken by FCC and the shared spectrum companyrespectively. It is clearly noticeable that only a few frequency bands are inuse while about 70% of the remaining spectrum (mainly belonging to legacyradio technologies) remains unused for longer periods of time [1, 2]. This iswhere the opportunistic spectrum access (OSA) comes into picture. ThroughOSA, users can utilize the spectrum currently being unused especially whenit comes to licensed spectrum of legacy technologies. One example is the TVspectrum. However, for a radio to use the spectrum opportunistically it shouldbe aware and intelligent enough to look out for such vacant spectrum bands.Hence there is a great need to build better and intelligent radios and this iswhere the phrase ‘cognitive radio’ comes from. Cognition is the psycholo-gical result of perception and reasoning. This term was first coined by Mitola[3] in his PhD research work, though lately this has become synonymouswith the term Dynamic Spectrum Access (DSA) in the sense that the goal ofDSA/OSA is achieved through the cognition of the radio.

Cognitive Radios (CRs) opportunistically cash in on the licensed spec-trum allocated to rightful owners that is not being used in time, frequency,space and code dimensions of a signal at a given instant (also called spec-tral opportunities) in order to make their communications efficient in termsof throughput, energy and delay metrics. Studies have shown that 90% ofthe time, the valuable licensed spectrum was found to be unoccupied [1].However, on the contrary, with the advent of portable gadgets, the unlicensedspectrum for technologies like Wi-Fi is being crowded most of the times.

Hence, dealing with Wi-Fi crowding phenomenon is critically importantfor sustainable wireless computing for our future generations. One of themost recent endeavors in this direction was made by FCC which approvedand reallocated the use of Television White Spaces (TVWS) for Wi-Fi. Suchrenovated Wi-Fi technology capable of using TVWS via cognition was re-named as White-Fi (IEEE standard 802.11af), sometimes also called ‘Wi-Fion Steroids’. TV channels 2–52 have been opened up for unlicensed usage bythe general public. Though the FCC recently has agreed to ditch the spectrumsensing requirement and instead encourage the use of online databases forspectrum vacancy [22, 23], it would still be an undeniable component whenconsidering an ‘on the fly’ ad hoc Wi-Fi network that does not have access tothese online databases.

Energy-Efficiency of Cooperative Sensing Schemes 57

Figure 1 FCC spectrum measurements.

In the field of CR technology, the rightful users of the licensed spectrumare termed the Primary Users (PUs) where as the other CR users trying touse this spectrum opportunistically are the Secondary Users (SUs). The SUs,before dynamically accessing this licensed spectrum should make sure that itis not being used by any PU in their local vicinity so as to avoid interferenceto the PUs. The key component to achieve this is the sensing of the spectrumwith high reliability.

As the transmitter based sensing techniques like energy detection [4, 5],matched filtering [6], cyclostationary [7] feature detection rely solely on thePU signal detection, there is a high chance for the cognitive user to be blindedby fading, shadowing and interference which might further degrade the accur-acy of these techniques. The affects of these degradations have been studiedin [8]. To overcome these blinding phenomena, cooperative sensing has beenfound to be far superior to just local/non-cooperative sensing as it solves thehidden node problem in addition to the others mentioned.

However, there is limited literature that looks at the energy cost aspectof the cognitive radio technology. One work that does and is our point of


Figure 2 Spectrum measurements in New York City and Chicago conducted by SharedSpectrum, 2005.

interest is [9] which looks at the positive and negative impact of CR MAClayer sensing in terms of energy. However, this work does not look at theenergy costs of cooperative sensing; and the techniques (optimal scan andgreedy scan schemes) proposed here are non-cooperative sensing schemes.Our work in this paper is a subsequence to that with a goal to minimizethe energy spent in spectrum sensing for each node and the network as awhole through cooperative sensing schemes. The following are the specificcontributions made in this paper:

• We developed an energy model to study and quantify the energy costsof a broader class of existing generic cooperative MAC layer sensingschemes – one based on a distributed architecture and one based on acentralized architecture.


• We proposed corresponding new α-schemes – α-distributed and α-centralized where only a fraction α of the nodes scan as opposed to allthe nodes in the generic distributed and centralized schemes.

• We numerically evaluated and compared the energy consumption costsof the generic distributed and centralized schemes against the proposedα-distributed and α-centralized schemes.

• We studied optimal values of α and number of nodes in the network N .• We made a conclusive energy comparison study of non-cooperative

sensing schemes and cooperative schemes.

The rest of the paper is organized as follows: related work is discussed inSection 2; an overview of the current sensing schemes and the proposed α-schemes is given in Section 3. In Section 4 we discuss the system modelbased on which further energy consumption analysis equations are developedin Section 5 and energy savings analysis done in Section 6. Numerical evalu-ations of these equations are done in Section 7 followed by an interpretationof their significance.

2 Related Work

This section gives a short overview of the prior work done in cognitive net-work cooperative sensing schemes with more emphasis placed on the twowell known CR cooperative sensing implementations – distributed and cent-ralized cluster based schemes. In a distributed cooperative sensing scheme,the SUs share the sensed information among themselves and make individualdecisions. The advantage here is that there is no need for a common receiverinfrastructure and high bandwidths [10]. Distributed collaboration schemesare discussed in [11]. In [12, 13] relay based cooperation are discussed wherea few SUs act as relays to other SUs. In [13], the Amplify and Relay (AR)and Detect and Relay (DR) schemes are proposed for sensor networks.

In a centralized cooperative sensing system model, there is a common re-ceiver which collects all the sensing information done by the SUs (CRs). Ourinterest is mainly on the cluster based schemes where the SUs are groupedinto clusters or teams for collaboration; the reason being that to design anenergy efficient cooperative sensing scheme, grouping would be a key com-ponent to cash in on the team collaboration instead of putting the burdenof sensing the huge spectrum on each SU [14]. By grouping the SUs intoclusters and selecting the most favourable SU in every cluster to report tothe common receiver, the sensing performance can be greatly enhanced [15].


In [16] a study is carried out on the optimal number of clusters required tominimize the communication overhead without loss in the detection perform-ance. In [17], two level hierarchical cluster based architecture is proposedwhere the low level collaboration is among the SUs within a cluster and highlevel collaboration is among the cluster heads chosen for each cluster. Othergrouping techniques are studied in [18–21].

Although many variations of cooperative sensing schemes exist, ourobjective is to study the amount of energy consumption in both these categor-ies. Also we propose the improved versions of both the generic distributedand centralized scheme and demonstrate the relative energy savings throughevaluations.

Most of the work done till to date on cooperative sensing in CR net-works mainly focus on increasing the throughput and spectrum sensingefficiency/accuracy. Not much has been done on analyzing how energyefficient these schemes are.

Also as there is no consensus over which specific scanning schemeperforms the best, we chose to look at a generic class of distributed andcentralized schemes and apply our energy model to evaluate their energyconsumption. The following section gives a brief overview of the existingsensing schemes and the proposed α-schemes.

3 Overview of Sensing Schemes

Spectrum sensing is a key critical component in the cognitive radio techno-logy since the ability of cognition is achieved through this spectrum sensingfunctionality of the CR. These spectrum sensing schemes can be roughlyclassified into two categories.

3.1 Non-Cooperative Sensing

Non-cooperative sensing schemes also called as local sensing schemes re-quire each node in the network to sense the spectrum for free channelsindividually. These nodes do not share the scanned information with theirneighbours and hence no reporting is involved in a non-cooperative sensingcycle. The non-cooperative sensing we use as reference in our work is theoptimal scan scheme from [9]. In this optimal scan scheme, every node hasto scan all the channels before choosing the optimal channel among them.


Figure 3 Cooperative sensing cycle.

3.2 Cooperative Sensing

In cooperative sensing schemes, all the nodes in the network sense/scan thespectrum and share this information with all the neighbouring nodes in thereporting phase (see Figure 3). This process reduces the CR blinding dueto interference, fading and hence increases the probability of PU detection.To be precise, the collaboration of SUs can either be used to increase thenumber of channels scanned or improve the detection probabilities by havingmultiple nodes scan a single channel. In this paper, we look at more of aparallel cooperative sensing [24] where all the nodes are designated differentchannels to be scanned. Each node individually scans the designated channelsin parallel (concurrently) and then convey this information through its sensingreports (SR).

Each sensing cycle (SC) has a scanning period (SP) and a reporting period(RP). Based on how the reporting/sharing is accomplished in the reportingperiod, cooperative sensing can be categorized into mainly two broad classesof architectures – distributed and centralized. The generic distributed sensingscheme we refer in this work belongs to the distributed architecture and ishereafter referred to as ‘distributed sensing scheme’ and the generic central-ized cluster based scheme belongs to the centralized architecture which ishereafter referred to as the ‘centralized cluster based scheme’.

3.2.1 Distributed Sensing SchemeIn the distributed sensing scheme as shown in Figure 4, each node scansits share of channels during the SP and shares this information with all itsneighbors in the RP.


Figure 4 Distributed scheme.

Figure 5 Centralized scheme.

3.2.2 Centralized Cluster Based Sensing SchemeIn the centralized cluster based scheme as shown in Figure 5, the wholenetwork of nodes can be divided into clusters (based on some higher layerprotocol). Each cluster has a cluster head (CH) which does not carry outthe scanning. Only the cluster members (CMs) in each cluster scan theirshare of the channels and convey this information to their respective CH.The CHs then share this information with the other remaining CHs in thenetwork. There are two levels of communication happening here, one at theintra cluster level and the other at the inter cluster level between the CHs. Atthe end of the inter cluster level information exchange, all the nodes in thenetwork have a global view of the channel information for the whole network(see Figure 5).


Figure 6 α-distributed scheme.

3.3 Proposed α-Sensing Schemes

Next, we propose the α-sensing schemes to make the conventional schemesmore energy efficient. In the α-sensing schemes only a fraction α of nodesshare the burden of scanning the channels in each sensing cycle. This isa form of load sharing which saves energy for the other fraction of nodesin that sensing cycle and simultaneously the scanning of all the channels iscollectively completed by the end of the sensing cycle. This fraction of nodescan be chosen based on their SNRs and PDRs (Probability Detection Ratios)to attain better spectrum sensing accuracies.

3.3.1 α-Distributed Sensing SchemeIn the α-distributed sensing scheme as shown in Figure 6, only an α fractionof nodes scan the channels in a given sensing cycle. However they still sharethis information with all their neighbouring nodes just similar to the genericdistributed sensing scheme. This saves energy, as each node has to scan onlyan α percentage of the times on average, in any given number of sensingcycles. This subset of α nodes can be chosen based on a probabilistic randomnumber generator. For every SP, each node, through a probabilistic method(random number generator) decides to participate in scanning if the generatedvalue is less than the ‘α’ value. This way on an average each node in thenetwork scans once in ‘(1/α)’ sensing cycles (see Figure 6).

3.3.2 α-Centralized Cluster Based Sensing SchemeIn this α-centralized sensing scheme as shown in Figure 7, instead of all theCMs in the cluster scanning for channels, only a fraction α of the CMs sharethe scanning responsibility and report this information to the CH. The CH inturn shares this information with other CHs similar to the centralized scheme.


Figure 7 α-centralized scheme.

Once the CHs receive all the other cluster scan information, each CH shares afinal report with its CMs. The fraction α of the CMs in each cluster is chosenby the CH.

Although another option of choosing a fraction α of the clusters insteadof fraction of CMs from each cluster is possible, keeping in considerationthe spatial diversity benefits of the clusters in the case of varying channelcharacteristics, it is better to have the scanning carried out in all the clustersfor better sensing accuracies.

To further study these schemes, the system model and the analyticalenergy model are developed in the next section.

4 System Model

4.1 Basic Common Aspects of the Cooperative Sensing Model

We envision a crowded ad hoc WLAN scenario where all the nodes areconnected in a clique network and hence are in the hearing range of eachother. Each node has two transceivers/radios – one completely dedicated forthe sensing and reporting purpose and the other radio for data transmission(see Figure 8). The radio for sensing and reporting shifts to the channel(s)that needs to be scanned during the SP and finally switches to the controlchannel for reporting purposes. The other physical radio for data transmissionswitches to the vacant channel over which it could transfer the data.

At the end of the SP, each node shares a sensing report with all the re-maining nodes through a single broadcast packet regardless of the numberof channels scanned. Since the nodes perform parallel scanning, at the endof the reporting period every node would have the spectrum map of all thechannels. We do not presume the existence of a fusion center in this ‘on


Figure 8 Time frame structures of scanning and reporting, data transmission respectively.

the fly’ network for both the distributed and centralized architectures. In thedistributed scheme, each node acts as a fusion centre for itself while in thecentralized scheme the cluster head can take up this role for its cluster.

4.2 Orchestration

The total number of channels to be sensed ‘C’ by the network of ‘N’ nodesare decided prior to the start of SC. Since there is no reporting involved in thenon-cooperative sensing scheme, each node scans all the C channels in thescanning period.

In the distributed cooperative sensing scheme, each node scans its share ofdesignated channels in the SP. In the RP, it broadcasts this information to its(N − 1) neighbors and similarly decodes the (N − 1) reports it receives fromits scanning neighbors. In the centralized scheme, each CM scans its shareof designated channels and sends an SR to the CH. The CH after collectingall the SRs of its CMs, broadcasts an SR with this scan information of itscluster to all the other CHs in the network. Similarly, after receiving all theSRs from its peer CHs, each CH then sends a final consolidated SR havingall the channel scan information to its CMs. Once these final SRs from thecorresponding CHs are shared, all the CMs and CHs have a global view of allthe channels scanned by the whole network.

4.3 Energy Model of Sensing Cycle

Energy consumed by each node per sensing cycle ES is given by the sumof the total energy to scan all the assigned channel ETscan , the total energy to


Table 1 Definition of variables used [9].Variable DefinitionPscan Power consumed to scan a channel (700 mW)Psw Power consumed to switch once between channels (750 mW)Ptx Power consumed to transmit a packet (750 mW)Prx Power consumed to receive a packet (750 mW)Tscan Time to scan a channel (50 ms)Tsw Time to switch once between channels (0.06 ms)Tdata Time to transmit a Data packet (0.08 ms)Escan Energy consumed to scan a channel = PscanTscanEsw Energy consumed to switch once between channels = PswTswEsrt Energy consumed to transmit a Sensing Report (SR) = PtxTdataEsrd Energy consumed to decode/receive a SR = PrxTdataC Number of channelsN Number of nodes in the networkNS Number of scanning nodes in the networkα Fraction factorK Number of clusters into which the whole network of N nodes is divided/groupedMS Number of scanning CMs

switch between these channels ETsw, the total energy to transmit/broadcastthe SR(s) to the other nodes ETx

and the total energy to receive the SRs fromall the other nodes ERx

.

ES = ETscan + ETsw + ETx+ ERx

Based on the above system and energy model developed, appropriateequations for energy consumption analysis are derived in the followingsection.

5 Energy Consumption Analysis of Sensing Schemes

5.1 Non-Cooperative Sensing Scheme

Since there is no reporting period in a non-cooperative sensing scheme, theenergy consumed by each node is just the sum of the energy to scan the des-ignated channels and the energy consumed to switch between those channels.Each node scans channels and hence has to switch times when hopping fromone channel to another. Hence

ESnon−coop = CEscan + (C − 1)Esw


where ESnon−coop is the energy consumed for each node during the scanning

period. Total energy consumed by all the N nodes in the network to sense C

channels in this non-cooperative sensing scheme is given by

Enon−coop = NESnon−coop

Enon−coop = NCEscan + N(C − 1)Esw (1)

5.2 Distributed Sensing Scheme

In this generic scheme, each node scans C/N(≥ 1) channels in each SP aslong as N > 1. If N > C, not every node has to scan the channels. Hence thetotal energy for the whole network in the distributed scheme is given by thefollowing generic equation:

Edist = NSESdist + (N − NS)E

NS

dist (2)

where NS = min(N,C) is the number of scanning nodes, ESdist is the energy

consumed by the scanning node, ENSdist is the energy consumed by the non-

scanning node. ESdist for a scanning node is the sum of energy to scan the

designated (C/NS) channels, switch in between those channels, transmit oneSR with the channel scan information and receive (NS − 1) SRs from theother scanning nodes. ENS

dist for a non-scanning node is the energy to decodeall the SRs received from the scanning nodes.

ESdist =

(C

NS

)Escan +

(C

NS

− 1

)Esw + Esrt + (NS − 1)Esrd (3)

ENSdist = NSEsrd (4)

Substituting equations (3) and (4) in (2) gives rise to the following energyequation for the whole network of nodes of distributed scheme

Edist = CEscan + (C − NS)Esw + NSEsrt + NS(N − 1)Esrd (5)

Since NS = min(N,C) we have the following two cases:

• If N ≤ C, then

Edist = CEscan + (C − N)Esw + NEsrt + (N2 − N)Esrd (6)

• If N > C, then only C nodes are required to scan

Edist = CEscan + CEsrt + (NC − C)Esrd (7)


5.3 α-Distributed Sensing Scheme

In this scheme, for a chosen value of α (0 < α ≤ 1), only αN nodes performthe scanning while the remaining nodes do not scan for that SP. Hence for agiven number of sensing cycles, the nodes in this scheme would have to scanonly for α percentage of the cycles on an average while they can save on theirenergy for the remaining (1 − α) percentage of the cycles.

Practically, since the sensing nodes αN cannot be either less than 1 or forthat matter greater than C, we arrive at the following bound for α:(

1

N

)≤ α ≤ min

(C

N, 1

)(8)

Because of this α bound we can completely rule out the possibility of αN >

C in this α-scheme.Substituting NS = αN in equations (2–4) gives the following en-

ergy equations for each of the scanning node and for the whole networkrespectively:

ESα−dist =

(C

αN

)Escan +

(C

αN− 1

)Esw + Esrt + (αN − 1)Esrd (9)

ESα−dist = CEscan + (C − αN)Esw + αNEsrt + α(N2 − N)Esrd (10)

where ESα−dist is the energy consumed by the scanning node and Eα−dist is the

energy consumed by the whole network of nodes.

5.4 Centralized Cluster Based Sensing Scheme

In this generic centralized scheme, the network of N nodes is divided into K

clusters, each cluster having a group of M+1 nodes such that N = K(M+1).Each cluster of M + 1 nodes thus has one cluster head (CH) and M clustermembers (CMs). The CMs alone do the scanning and send their SRs to theirrespective CHs. Each CH then shares this information with the remainingCHs. A final SR is then broadcasted from the CH to its CMs.

Each cluster has to scan (C/K)(≥ 1) channels and hence the energyconsumed for each cluster per sensing cycle is

ECcent = ECH

cent + MSEScent + (M − MS)E

NScent (11)

where MS = min(M,C/K) is the number of scanning CMs, ECHcent is the

energy consumed by the CH, EScent is the energy consumed by the scanning

CM, ENScent is the energy consumed by the non-scanning CM.


Each CH transmits K SRs – one SR containing the scanned channel in-formation of the cluster is unicast to each of the remaining (K − 1) CHsand one SR is broadcast back to the CMs after receiving all SRs from the(K − 1) CHs. Thus each CH has to decode all the MS SRs from its CMs andK − 1) SRs from the other CHs. For simplicity of evaluation, we considera basic access mode of IEEE 802.11 [29] without RTS/CTS and ignore theenergy for the ACK in the case of unicast transmission. For simplification,we further ignore the energy for the DIFS.

ECHcent = KEsrt + (MS + (K − 1)Esrd (12)

Each CM transmits an SR to the CH after scanning (C/KMS) channels anddecodes the final SR that it receives from its CH.

EScent =

(C

KMS

)Escan +

(C

KMS

− 1

)Esw + Esrt + Esrd (13)

The energy consumed by the non-scanning CMs is

ENScent = Esrd (14)

Ecent = KECcent (15)

(15) Substituting equations (11–14) in (15) gives the energy equation for thewhole network of nodes in the centralized scheme.

Ecent = CEscan + (C − KMS)Esw + K(MS + K)Esrt

+ K(MS + M + K − 1)Esrd (16)

Similar to the distributed scheme, if M > (C/K) then not every CM has toscan in the cluster and hence we have the following two cases:

• If M ≤ (C/K), then

Ecent = CEscan + (C − KM)Esw + K(M + K)Esrt

+ K(2M + K − 1)Esrd (17)

• If M > (C/K), then

Ecent = CEscan + (C + K2)Esrt + (C + K(M + K − 1))Esrd

+ K(2M + K − 1)Esrd (18)


5.5 α-Centralized Cluster Based Sensing Scheme

In this scheme, only αM CMs in each cluster do the scanning while theremaining (M − αM) CMs do not scan for that SP.

αM can neither be less than 1 and nor can it be greater than (C/K).(C/K) is the number of assigned channels for each cluster which would bethe required number of scanning nodes too. Translating this to a mathematicalbound gives the following:

(1

M

)≤ α ≤ min

(C

KM, 1

)(19)

Because of this α bound we can completely rule out the possibility of MS >

(C/K) in this scheme.Substituting MS = αM in equations (11–15) gives the following energy

equation for the whole network of nodes in the α-centralized scheme:

Eα−cent = CEscan + (C − KαM)Esw + K(αM + K)Esrt

+ K((1 + α)M + (K − 1)Esrd (20)

In the subsequent section, we analyze the energy savings and optimal valuesof α and N based on the above derived equations.

6 Energy Savings and Optimal Values

6.1 Energy Savings

Lemma 1. Distributed cooperative sensing scheme is more energy-efficientthan a non-cooperative scheme only when the number of nodes N is greaterthan 1 and the communication energy is less than

(NC − C)Escan + (NC − N − C + NS)Esw

NNS

Proof. The distributed scheme saves energy over the non-cooperative schemeif and only if the total energy consumption for whole of network of nodes inthe distributed scheme is less than the total energy consumption for the samenetwork of nodes in the non-cooperative scheme. This is represented by thefollowing relation:

Edist ≤ Enon−coop (21)


Since communication is possible only when the network has more than onenode, for the distributed scheme to be valid and equation (20) to hold, thefollowing condition should be met:

N > 1

Solving equation (20) using equations (1) and (5) gives the followingcondition for communication energy:

Esrc ≤ (NC − C)Escan + (NC − N − C + NS)Esw

NNS

where Esrc = Esrt = Esrd, NS = min(N,C) for the distributed scheme andNS = min(αN,C) for the α-distributed scheme.

For ease of simplification, Esrt, Esrd in equation (5) are jointly denoted byEsrc which is the communication energy in general.

Lemma 2. Centralized cluster based cooperative sensing scheme is energy-efficient than a non-cooperative scheme only when the number of clusters andthe number of cluster members is at least 1 and the communication energy isless than

(NC − C)Escan + (NC − N − C + KMS)Esw

K(2MS + 2K + M − 1)

Proof. The centralized scheme saves energy over the non-cooperative schemeif and only if the total energy consumption for whole of network of nodes inthe centralized scheme is less than the total energy consumption for the samenetwork of nodes in the non-cooperative scheme. This is represented by thefollowing relation:

Ecent ≤ Enon−coop (22)

For a network to form a cluster, there should at least be one cluster and onecluster member in the cluster and hence we have

K ≥ 1, M ≥ 1

Solving equation (21) using equations (1) and (16) gives the followingcondition for the communication energy:

Esrc ≤ (NC − C)Escan + (NC − N − C + KMS)Esw

K(2MS + 2K + M − 1)

where Esrc = Esrt = Esrd, MS = min(M,C/K) for the centralized schemeand MS = min(αM,C/K) for the α-centralized scheme.


6.2 Optimal α Values for the α-Distributed Scheme

6.2.1 Optimal α for Maximum Energy SavingsThe optimal α for given N is defined as the value of α where the energysavings of the α-distributed scheme over the distributed are the maximum.The energy savings can be looked at, from two different perspectives – theenergy savings for the whole network of nodes and the energy savings perscanning node in the network. We first look at the optimal α for maximumenergy savings considering the whole network of nodes over one sensingcycle paired with various constraints to form a set of optimization problems.

• Optimization Problem 1 – Optimal α for a whole network of nodes:

Maximize f (α) =(

Edist − Eα−dist

Edist

)

such that

(1

N

)≤ α ≤ min

(C

N, 1

)

The α value we consider optimal here, is the value of α where theα-distributed scheme shows the maximum energy savings over the dis-tributed scheme considering the whole network of nodes for a givensensing cycle. f (α) is maximized at α = (1/N) which thus becomes theoptimal α. However, considering the shadowing phenomenon, batterycharacteristics of the wireless nodes and most importantly the limitedscanning and reporting periods, this value should be chosen with discre-tion in order to avoid poor spectral efficiencies and accuracies, shorteroperating lifetimes respectively [28]. Hence a constraint to limit thesensing and reporting time in a given sensing cycle is needed as shownbelow in the next optimization problem.

• Optimization Problem 2 – Optimal α for a whole network of nodes withtime constraint:

Maximize f (α) =(


Edist

)

such that

(1

N

)≤ α ≤ min

(C

N, 1

)and L ≤ l

where L is the total time for the SC as defined below:

L =(

C

αN

)Tscan +

(C

αN− 1

)Tsw + αNTdata (23)


In the evaluation section, we plot the optimal values where f (α) ismaximized and the constraint L ≤ l ms is satisfied.Also, for further study of the relative energy cost comparison of a scan-ning node in distributed scheme versus a scanning node in α-distributedscheme, we maximize the function f (α) with a scanning node energyconstraint.

• Optimization Problem 3 – Optimal α for a whole network of nodes withper scanning node energy constraint:

Maximize f (α) =(


Edist

)

such that

(1

N

)≤ α ≤ min

(C

N, 1

)and g(α) ≥ 0

where

g(α) =(

ESdist − ES

α−dist

ESdist

)

The g(α) ≥ 0 constraint was taken into account considering the factthat for a given sensing cycle, although the α-distributed scheme savesenergy for the network of nodes N on the whole, it should not burdeneach scanning node with a very high number of channels to be scanned,causing the node to die quicker. This constraint makes sure that theenergy of the scanning nodes in the α-distributed scheme is either lessthan or at least equal to the energy of scanning node in the distributedscheme. The optimal α with this constraint is always the upper bound ofα given by min(C/N, 1). However if the constraint is relaxed to be lessthan zero, i.e., g(α) ≤ 0, the optimal would move to the lower boundwhich is (1/n). g(α) thus helps to explain the fact that the per scanningnode energy cost of α-distributed scheme versus that of the distributedover one sensing cycle is always higher except at min(C/N, 1) where itequals the distributed. In the next optimization problem, we show thatthe energy savings over a cumulative n sensing cycle period are howeverpositive.

• Optimization Problem 4 – Optimal α for maximum energy savings overn sensing cycle period:

Maximize f (α) =(


Edist

)


such that

(1

N

)≤ α ≤ min

(C

N, 1

)and h(α) ≥ 0

where

h(α) =(

min(

CN

, 1)EdistS − (αES

α−dist)

min(

CN

, 1)ES

dist

)

The constraint h(α) defines that, for a given n sensing cycle periodeach scanning node in the distributed scheme would have to scanmin(C/N, 1) × n times on an average while the scanning node in theα-distributed scheme would have to scan only for α×n times on average.With this new constraint, the optimal α value is still (1/N). However,the numerical evaluation results of h(α) show that the constraint itselfresults in positive values unlike the constraint g(α). This goes on toshow that the α-distributed scheme saves energy from a scanning node’sperspective as well as for the whole network over a given period of n

sensing cycles and more noticeably at smaller α values.

6.2.2 Optimal N for Maximum Energy SavingsIt is also interesting enough to analyze if there is an optimal N for a given α

where the energy savings of the α-distributed over distributed are maximum.Hence we derive the optimal values of N for given fixed values of α bymaximizing the function F(N) where

F(N) =(


Edist

)

and solving it for maximization shows that it is maximized at

N =max

(−Escan + √

E2scan + EswEscan + (

Cα

)EsrcEscan + (

Cα

)EswEsrc

Esrc, C

)

Similarly, the function

G(N) =(

min(

CN

, 1)ES

dist − (αESα−dist)

min(

CN

, 1)ES

dist

)

for highest magnitude of energy savings per scanning node over n sensingcycles is maximized at N = C. We plot the values showing the trend ofoptimal N over a varying range of a for the functions F(N) and G(N)

separately in the next section.


The outcomes of all the above optimizations are completely dependenton α, which is the basis of the relation between distributed and α-distributed.Since this relation remains the same between centralized and α-centralized,the optimization results and hence the inferences are going to be similar. Sowe do not look at optimizations for the centralized schemes in this work.

7 Evaluation

We do a numerical evaluation for all the proposed generic equations andshow the energy savings of the α-schemes over their counterparts. All thebase values for Escan, Esw, Esrt, Esrd are calculated from equations and valuesspecified in [9, table 1]. Following [25] where White-Fi has to scan at leastabout 50 TV channels and [26] where the notion of channels can just be subbands obtained by dividing a given wide band, we believe C = 100 wouldbe a suitable and practical value for the number of channels to be scanned. In[27] the authors show that the optimal sensing time for a SU to detect the PUwith 90% probability is about 15 ms and in [28] the false alarm probabilityhad a linear down trend as scan time was varied from 20 to 100 ms. So weinfer that Tscan = 50 ms would be an appropriate value to achieve a gooddetection probability and low false alarm rates simultaneously. We evaluatethe total energy consumed for each of the schemes by varying the range ofnumber of nodes N and the fraction factor α.

7.1 Distributed vs. α-Distributed Scheme

Figure 9 shows the energy trends over a varying N for the distributed andα-distributed schemes. The lower the value of α, the lesser are the energycosts for the α-distributed scheme. These energy savings become more ap-parent for higher node densities. However at the point the energy cost ofthe α-distributed scheme equals the distributed scheme and hence the energysavings decrease from positive values to zero. This is due to the fact thatthe significance of the fraction factor α lies only in the range suggested inequation (6), further explaining the point that there is no reason to have scan-ning nodes greater than the required number, which would be the number ofchannels C for both the distributed and the α-distributed schemes. Hence ourproposed α-distributed scheme holds significance as long as αN < C.

Figure 10 shows that the average energy costs of a node for both dis-tributed and α-distributed keep decreasing with increasing node densities. Acloser analysis indicates that this is due to the reduction in the scanning en-


Figure 9 Total energy consumption of whole network of N nodes in distributed andα-distributed schemes.

Figure 10 Average energy consumption of each node in distributed and α-distributed schemes.


Figure 11 Optimal values of α where the energy savings of the α-distributed scheme over thedistributed scheme are maximum, for a given N and L.

ergies; since with increasing node densities, the number of channels scannedon an average by each node keeps decreasing. Though the reporting energyincreases on an average, this increase is greatly offset by the decrease in thescanning energy since Escan � Esrt (or) Esrd.

7.2 Optimal Values

The optimal α values for a given N where f (α) is maximized and the con-straint of the sensing cycle time length L is satisfied are shown in Figure 11.It can be clearly noticed that the optimal α values decrease with increasing L.With higher L each node gets to scan more number of channels and so lesserscanning nodes are needed which results in a smaller α.

A further study of optimal values of N for a given α can be carried outusing Figures 12 and 13. The function F(N) has the highest magnitude ofenergy savings at various values of N for varying α until α = 0.5, afterwhich the optimal N stays at 100 (value of C). Optimal N for the functionG(N) is always at N = C = 100 regardless of the value of α. The energysavings for both and predictably go down with increasing α values.


Figure 12 Percentage of energy savings and optimal N values where F(N) is maximized.

Figure 13 Percentage of energy savings and optimal N values where G(N) is maximized.


Figure 14 Total energy consumption for whole network of N nodes in centralized and α-centralized schemes.

7.3 Centralized vs. α-Centralized Schemes

Figure 14 shows the energy trends over a varying N for the centralizedand α-centralized schemes. As expected, the centralized schemes in generalhave lower energy costs than the distributed schemes and the α-centralizedschemes have lower energy costs over the centralized scheme.

The α-centralized schemes have lower energy costs with decreasing aand this can attributed to the lesser control overheads both for the CH andthe CMs. Also, the energy increase with increasing N is more linear in thecentralized schemes while this increase is inclined towards being exponentialin the distributed schemes. This clearly shows that centralized schemes ingeneral are more energy efficient and hence should be the first choice athigher N values. The values used in this plot were derived for K = 1. To gainfurther insight into the impact of K on energy consumption, we use Figure 15which shows that a higher K results in higher energy overhead.


Figure 15 Impact of K on the total energy consumption for whole network of N nodes incentralized and α-centralized schemes.

7.4 Non-Cooperative vs. Cooperative Schemes

Cooperative schemes not only reduce the bandwidth requirements to conveythe scanning information but also the energy consumed to scan and sharethis information. Figure 16 proves this claim and it can be noticed that alogarithmic scale was used to capture the wide variation of the energy valuesof non-cooperative schemes and the lower energy values of the cooperativeschemes.

8 Conclusions

The energy model of sensing developed in this work gives a platform for anenergy accountability, quantification and comparison of the non-cooperativesensing schemes and the generic cooperative sensing schemes – distributedand centralized along with our proposed new α-schemes. Our investigation ontheir energy costs shows that the cooperative schemes easily outperform thenon-cooperative scheme and further the α-schemes are significantly energy


Figure 16 Energy consumption comparison of the non-cooperative and cooperative schemes.

efficient than the generic schemes. Optimal values for the fraction factor α

and number of nodes N derived contribute to further useful insights on therelative energy savings.

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Biographies

Reshma Syeda is currently a graduate student at Wichita State University,pursuing her M.S. degree in Electrical Engineering under the supervision ofProfessor Vinod Namboodiri. She has also worked as a graduate researchassistant at the Cisco Technical Research Center of WSU. She receivedher B.Tech. degree in Electronics and Communications Engineering fromJawaharlal Nehru Technological University, India in 2007. Her researchinterests include cognitive radio networks and smart grids.

Vinod Namboodiri is currently an Assistant Professor at the Department ofElectrical Engineering and Computer Science at Wichita State University,USA. He graduated with a Ph.D. in Electrical and Computer engineeringfrom the University of Massachusetts Amherst in 2008. He has served oris currently serving on the technical program committees of IEEE GLOBE-COM, IEEE ICC, IEEE IPCCC, and IEEE GREENCOM, and is an activereviewer for numerous journals and conferences in the mobile computingand green communications areas. His research interests include designing al-gorithms and protocols for energy-intelligent and sustainable computing, anddesigning an effective communication architecture for smart electric grids.In the past he has worked on designed MAC and routing protocols, anddeveloping energy-efficient protocols and algorithms for different wirelesstechnologies like Wireless LANs, RFID Systems, Wireless Sensor Networks,and Wireless Mesh Networks.

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